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"... Category theory plays an important role as a unifying agent in a rapidly expanding universe of mathematics. In this paper, an introduction is given to the basic denitions of category theory, as well as to more advanced concepts such as adjointness, factorization systems and cartesian closedness. ..."
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Category theory plays an important role as a unifying agent in a rapidly expanding universe of mathematics. In this paper, an introduction is given to the basic denitions of category theory, as well as to more advanced concepts such as adjointness, factorization systems and cartesian closedness. In the past decades, the subject of mathematics has experienced an explosive increase both in diversity and in the sheer amount of published material. (E.g., the Mathematical Reviews volume of 1950 features 766 pages of reviews, compared to a total of 4550 pages in the six volumes for the rst half of 2000.) It has thus become inevitable that this growth, taking place in numerous and increasingly disconnected branches, be complemented by some form of unifying theory. There have been attempts at such unications in the past, such as Birkhostyle universal algebra or the encyclopedic work of Bourbaki. However, the most successful and universal approach so far is certainly the theory of cat...
Submodule Algebras
"... this paper about submodules can be done with a slightly more general assumption that the category is given with the factorization system. This definition will be the central point of this paper and all other notions are derived from that and the requirement of finite completeness and finite cocomple ..."
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this paper about submodules can be done with a slightly more general assumption that the category is given with the factorization system. This definition will be the central point of this paper and all other notions are derived from that and the requirement of finite completeness and finite cocompleteness.
Journal of Pure and Applied Algebra 168 (2002) 147–176 www.elsevier.com/locate/jpaa
, 1999
"... This paper begins with the observation that the category of crossed modules is tripleable ..."
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This paper begins with the observation that the category of crossed modules is tripleable